I feel like the story is more important in TES than in Fallout, really.
In all fairness the story of Fallout 3 was only "VERY important" because of my prior knowledge of the Fallout universe, the game itself did absolutely nothing to highlight exactly what mass purification of an entire lake and area would mean beyond "trust us ok!".
While New Vegas I couldn't have cared less... Ohh my... land dispute... and they try to grandiose it up and fail miserably. It never stops seeming like a land dispute for a city and a power plant you don't care about. "Ohhh no! This might... cause a mild issue for a few years!". Which STILL could have worked if they made Vegas appealing, but they make it feel like such a sack of scum. The ONLY thing the story has going for it is that it made it personal, which it never really follows up on.
While Skyrim and Oblivion was the exact opposite problem. It sounded absolutely awesome and ground breaking. You knew you had something monumental on your hands that will shake the very fabric of the world for better or worse AND!!!... well... it meant absolutely nothing. Either the danger is pretty happy to sit on its butt or solving the issue feels really lack luster.
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So no, I honestly think it isn't that the story is more important in either of them.
I just think the 3d Fallout games have an issue with making the story feel as epic as it should be. While the Elder Scroll games (well last two ones anyhow) always feel extremely epic until you find out they really aren't.
Mind you, before you jump down my throat. I always usually avoided winning the games if only because the side quests are usually a lot more interesting (AND in three of those games... there is a penalty for winning)